454 research outputs found
On units of central division algebras over algebraic number fields
Der erste Teil meiner Diplomarbeit beschĂ€ftigt sich mit algebraischen Zahlkörpern. Um mehr ĂŒber den Zahlkörper zu erfahren, betrachtet man seine VervollstĂ€ndigungen bezĂŒglich seiner inĂ€quivalenten Bewertungen gleichzeitig. Die geeignete Methode hierfĂŒr sind die Adele und Idele. Man kann den Körper kanonisch als diskreten Unterring der Adele auffassen und erhĂ€lt des weiteren, dass die Adele modulo dem Körper kompakt sind. Ebenso kann man die Einheiten des Körpers als Unterring der Idele auffassen. Damit kann man beweisen, dass die Norm eins Idele modulo der Einheitengruppe des Körpers kompakt sind. Daraus lĂ€sst sich der Dirichletsche Einheitensatz sowie die Endlichkeit der Klassenzahl folgern.
Im zweiten Teil werden die Ideen des ersten Teiles auf den Fall von endlich dimensionalen Algebren ĂŒbertragen. Wie im Fall des Zahlkörpers erhĂ€lt man, dass die Adele modulo der Algebra kompakt sind. Im Fall der Gruppe der Idele muss man sich auf Divisionsalgebren beschrĂ€nken. Wiederum erhĂ€lt man, dass die Idele mit Norm eins modulo der Einheitengruppe der Divisionsalgebra kompakt sind. Damit lĂ€sst sich eine Verallgemeinerung des Dirichletschen Einheitensatzes beweisen, nĂ€mlich dass die Einheitengruppe einer Ordnung einer Divisionsalgebra endlich erzeugt ist.In the first part of my thesis I study algebraic number fields. To do so I introduce valuations and completions. The aim is to find out more about an algebraic number field by studying its completions simultaneously. The natural language to deal with the completions is that of adeles and ideles. There is an embedding of the field into the ring of adeles and one can show, that the ring of adeles modulo this field is compact. When studying the unit group of the adeles, which is the group of ideles, one can prove something similar. In fact one shows that the group of norm one ideles modulo the field is compact. This leads to a proof of Dirichlets Unit Theorem and one can show the finiteness of the class number, which are both important results in algebraic number theory.
The second part of my thesis generalizes the methodological approach introduced in the first part. As in the case of a field, one has that the adele ring of an algebra modulo the algebra itself is compact. When turning our attention to the group of ideles, one has to restrict to the case of a division algebra. One can define the norm one ideles and show that the group of norm one ideles modulo the division algebra itself is compact. Using this result one can generalize Dirichlets Unit Theorem and show that the unit group of an order of a division algebra is finitely generated
Tennessee Williams, the Playwright-Painter: Vieux Carré and Something Cloudy, Something Clear at the Crossroads between Text and Image
âSnatching the eternal out of the desperately fleeting is the great magic trick of human existenceâ, Tennessee Williams wrote in 1951 in an essay devoted to The Rose Tattoo, entitled âThe Timeless World of a Playâ (61). What the statement reveals is the American playwrightâs conception of art as a means of fighting against the passing of time, against the âawful sense of impermanenceâ (61) that never stopped haunting him. But the stage is not the only place where, as Williams wrote in the same essay, âtime is arrested in the sense of being confinedâ (61). The sketches and paintings he made throughout his life reveal the same obsession with time, the same desire to freeze the intensity of the moment into the work of art. Two paintings, made in 1975 and 1977, shed new light on two of his late plays, Vieux CarrĂ© and Something Cloudy, Something Clear. Written at the end of his life, both plays are attempts at capturing the totality of experience. In them, Williams intertwines past and present, life and art, combining movement and stasis to achieve a synthesis his paintings echo, or mirror, though in a very different way. The examination of these unknown paintings in relation to the plays is meant to engage us in a dialogue between texts and images. What the dialogical perspective reveals is a temporality that is circular rather than linear, anachronistic rather than chronological. Williams the painter and Williams the playwright blur the limits of space and time to reach that region where the distinctions between text and image collapse as one becomes the mirror of the other, its âhorizon,â as Jean-Luc Nancy writes in Au Fond des images. There, words fail and figures dissolve; there, silence and haziness confront the reader/spectator with the timelessness of art, not as something eternal or transcendent, but rather as a magic interval where the intensity of the vanishing moment can be captured. In the scripts of his plays as well as in his paintings, Williams faces us with the mystery of time, with an elusiveness that he considers as the only true essence of his art. Through a comparative analysis of two of his paintings with two of his late plays, I intend to show how the verbal and the visual interconnect in Williamsâs art, how his texts as well as his paintings convey a sense of âintense immobilityâ that is the artistâs way of beating âthe game of being against non-beingâ (Williams 2009, 61).« Snatching the eternal out of the desperately fleeting is the great magic trick of human existence » : Tennessee Williams Ă©crivit cette phrase en 1951 dans un essai intitulĂ© « The Timeless World of a Play » (61). Lâaffirmation met au jour une conception de lâart comme moyen de lutter contre le passage du temps, contre une « affreuse sensation dâimpermanence » (61) qui nâa jamais quittĂ© le dramaturge. Or, la scĂšne nâest pas le seul endroit oĂč, selon Williams, « le temps, soudain pris au piĂšge, sâarrĂȘte » (61). Les dessins et tableaux quâil rĂ©alisa tout au long de sa vie trahissent la mĂȘme hantise du temps qui passe, le mĂȘme dĂ©sir de fixer lâintensitĂ© du moment dans lâĆuvre dâart. Deux tableaux, peints en 1975 et 1977, permettent ainsi de porter un regard nouveau sur deux piĂšces Ă©crites Ă la fin de sa carriĂšre. IntitulĂ©es Vieux CarrĂ© et Something Cloudy, Something Clear, elles ont ceci de commun quâelles apparaissent comme des tentatives de capturer la totalitĂ© dâune existence, dâenfermer la petite Ă©ternitĂ© dâune vie dans les limites de la reprĂ©sentation. Dans chacune dâelles, Williams mĂȘle le passĂ© et le prĂ©sent, la vie et lâart, combinant les notions de mouvement et de stase pour opĂ©rer une synthĂšse dont ses images peintes sont lâĂ©cho, ou, pourrait-on dire aussi, le miroir. Lâanalyse de ces deux piĂšces au prisme de deux peintures mĂ©connues de Williams invite Ă un dialogue fructueux entre les textes et les images. De cette approche dialogique Ă©merge une temporalitĂ© plus circulaire que linĂ©aire, plus anachronique que chronologique. Williams le peintre et Williams le dramaturge brouillent les limites spatio-temporelles pour crĂ©er ce lieu intermĂ©diaire oĂč les distinctions entre texte et image sâannulent, lâun devenant le miroir de lâautre, son « horizon dâinterprĂ©tation », pour reprendre lâexpression de Jean-Luc Nancy. LĂ , les mots manquent et les formes sâĂ©vanouissent ; lĂ encore, le silence et lâindistinction confrontent le spectateur Ă lâintemporalitĂ© de lâart, non pas comme quelque chose dâĂ©ternel ou de transcendant, mais plutĂŽt comme un intervalle magique oĂč lâintensitĂ© du moment fuyant se rĂ©vĂšle, comme une Ă©vanescence capturĂ©e dans les mailles de la reprĂ©sentation. Dans les textes de ses piĂšces, comme dans ses tableaux, Williams met le spectateur/lecteur face au mystĂšre du temps, de ce temps objet dâune quĂȘte artistique vitale dans une Ćuvre oĂč les images nâont jamais cessĂ© dâaccompagner les mots
Quand le thĂ©Ăątre sâinspire du cinĂ©ma : Jean Cocteau, SergueĂŻ Eisenstein et Tennessee Williams
La fascination de Tennessee Williams pour le cinĂ©ma a laissĂ© des traces dans son thĂ©Ăątre. Les projections sur Ă©cran envisagĂ©es dans les indications scĂ©niques de The Glass Menagerie ou lâimportance accordĂ©e Ă la musique dans nombre de ses piĂšces nâen sont que quelques illustrations. Or, au delĂ du simple apport technique, les avancĂ©es de lâart cinĂ©matographique de la premiĂšre moitiĂ© du XXe siĂšcle invitent Ă repenser le rapport entre le rĂ©el et sa reprĂ©sentation, rapport que Williams nâa cessĂ© dâexplorer tout au long de sa carriĂšre. Ses Ă©crits autobiographiques sont parsemĂ©s de rĂ©fĂ©rences Ă des films et Ă des rĂ©alisateurs qui ont jouĂ© un rĂŽle essentiel dans lâĂ©laboration de son « nouveau thĂ©Ăątre plastique ». Lâanalyse de sa piĂšce la plus connue, A Streetcar Named Desire, Ă la lumiĂšre de ces Ă©crits rĂ©vĂšle des influences diverses. Cocteau et Eisenstein affleurent ainsi Ă la surface de lâĂ©criture dans une piĂšce oĂč les univers des deux rĂ©alisateurs se rencontrent, ouvrant de nouvelles perspectives dâinterprĂ©tation sur une Ćuvre dont il reste encore beaucoup Ă dĂ©couvrir.Tennessee Williamsâs lifelong fascination with cinema left marks on his theatre. The use of projections in The Glass Menagerie and the role played by music in many of his plays are cases in point. Yet, the influence of cinema on Williamsâs writing goes far beyond the mere transposition of new technological devices onto the stage. For cinema brought about new ways of representing the world, thus providing the playwright with the means of escaping from the realist tradition and creating the ânew, plastic theatreâ he advocated as early as 1944. His autobiographical essays are peppered with references to famous filmmakers who helped him shape his language for the stage. The examination of his most famous play â A Streetcar Named Desire â reveals the influence of Cocteau and Eisensteinâs films and theories, giving us a new insight into Williamsâs creative process
Unveiling age-independent spectral markers of propofol-induced loss of consciousness by decomposing the electroencephalographic spectrum into its periodic and aperiodic components
Background: Induction of general anesthesia with propofol induces radical changes in cortical network organization, leading to unconsciousness. While perioperative frontal electroencephalography (EEG) has been widely implemented in the past decades, validated and age-independent EEG markers for the timepoint of loss of consciousness (LOC) are lacking. Especially the appearance of spatially coherent frontal alpha oscillations (8-12 Hz) marks the transition to unconsciousness.Here we explored whether decomposing the EEG spectrum into its periodic and aperiodic components unveiled markers of LOC and investigated their age-dependency. We further characterized the LOC-associated alpha oscillations by parametrizing the adjusted power over the aperiodic component, the center frequency, and the bandwidth of the peak in the alpha range.
Methods: In this prospective observational trial, EEG were recorded in a young (18-30 years) and an elderly age-cohort (>= 70 years) over the transition to propofol-induced unconsciousness. An event marker was set in the EEG recordings at the timepoint of LOC, defined with the suppression of the lid closure reflex. Spectral analysis was conducted with the multitaper method. Aperiodic and periodic components were parametrized with the FOOOF toolbox. Aperiodic parametrization comprised the exponent and the offset. The periodic parametrization consisted in the characterization of the peak in the alpha range with its adjusted power, center frequency and bandwidth. Three time-segments were defined: preLOC (105 - 75 s before LOC), LOC (15 s before to 15 s after LOC), postLOC (190 - 220 s after LOC). Statistical significance was determined with a repeated-measures ANOVA.
Results: Loss of consciousness was associated with an increase in the aperiodic exponent (young: p = 0.004, elderly: p = 0.007) and offset (young: p = 0.020, elderly: p = 0.004) as well as an increase in the adjusted power (young: p < 0.001, elderly p = 0.011) and center frequency (young: p = 0.008, elderly: p < 0.001) of the periodic alpha peak. We saw age-related differences in the aperiodic exponent and offset after LOC as well as in the power and bandwidth of the periodic alpha peak during LOC.
Conclusion: Decomposing the EEG spectrum over induction of anesthesia into its periodic and aperiodic components unveiled novel age-independent EEG markers of propofol-induced LOC: the aperiodic exponent and offset as well as the center frequency and adjusted power of the power peak in the alpha range
The Thrombopoietin Receptor Agonist Eltrombopag Inhibits Human Cytomegalovirus Replication Via Iron Chelation
The thrombopoietin receptor agonist eltrombopag was successfully used against human cytomegalovirus (HCMV)-associated thrombocytopenia refractory to immunomodulatory and antiviral drugs. These effects were ascribed to the effects of eltrombopag on megakaryocytes. Here, we tested whether eltrombopag may also exert direct antiviral effects. Therapeutic eltrombopag concentrations inhibited HCMV replication in human fibroblasts and adult mesenchymal stem cells infected with six different virus strains and drug-resistant clinical isolates. Eltrombopag also synergistically increased the anti-HCMV activity of the mainstay drug ganciclovir. Time-of-addition experiments suggested that eltrombopag interfered with HCMV replication after virus entry. Eltrombopag was effective in thrombopoietin receptor-negative cells, and the addition of Fe3+ prevented the anti-HCMV effects, indicating that it inhibits HCMV replication via iron chelation. This may be of particular interest for the treatment of cytopenias after hematopoietic stem cell transplantation, as HCMV reactivation is a major reason for transplantation failure. Since therapeutic eltrombopag concentrations are effective against drug-resistant viruses, and synergistically increase the effects of ganciclovir, eltrombopag is also a drug-repurposing candidate for the treatment of therapy-refractory HCMV disease
Training Schrödingerâs cat: quantum optimal control
It is control that turns scientific knowledge into useful technology: in physics and engineering itprovides a systematic way for driving a dynamical system from a given initial state into a desired targetstate with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantumtechnologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantumenhancedsensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry,magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantumsimulation. In this communication, state-of-the-art quantum control techniques are reviewed and putinto perspective by a consortium of experts in optimal control theory and applications to spectroscopy,imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketcha roadmap for future developments
Not dear neighbours: Antennation and jerking, but not aggression, correlate with genetic relatedness and spatial distance in the ant Lasius niger
1. Neighbourâstranger response differences (NSRDs) are when individuals are either more aggressive (âNasty Neighbourâ) or less aggressive (âDear Enemyâ or âDear Neighbourâ) to direct neighbours than to other competitors perceived as âstrangersâ by the residents. Such effects are often reported in ants which, being fixed-location central-place foragers, may compete directly with their neighbours for resources or raid each other for brood. Overlayed onto this are potential spatial distance and relatedness effects on aggression, which are often not differentiated from NSRDs.
2. The literature on NSRDs and distance effects in ants does not reveal a systematic pattern across all ants due to their diversity of life histories, requiring each species to be evaluated individually. Lasius niger is a common Eurasian ant species, which can form very dense populations of colonies and shows pronounced nestmate recognition, so may be expected to show NSRDs.
3. Here, we take advantage of a semi-regular colony array to examine the effect of spatial distance and relatedness on aggression and probe for NSRDs.
4. Overt aggression does not vary with relatedness or spatial distance, and there is no evidence that direct neighbours represent a special case in terms of aggression. However, antennation and jerking decrease between less related and more spatially distant pairs, but are almost completely absent from allospecific interactions.
5. We tentatively propose that antennation and jerking together represent a ânegotiationâ phase, which may either precede or reduce the need for overt aggression. While a Nasty Neighbour effect might occur, a Dear Neighbour effect is unlikely in this species, and overall NSRDs do not play a large role in the ecology of this species. More broadly, this work highlights the importance of considering non-overtly aggressive responses when studying NSRDs
Towards assembling the internal ice stratigraphy in coastal regions of Dronning Maud Land, East Antarctica
The internal ice stratigraphy as imaged by radar is an integrated archive of the atmospheric- oceanographic, and ice-dynamic history that the ice sheet has experienced. It provides an observational constraint for ice flow modeling that has been used for instance to predict age-depth relationships at prospective ice-coring sites in Antarcticaâs interior. The stratigraphy is typically more disturbed and more difficult to image in coastal regions due to faster ice flow. Yet, knowledge of ice stratigraphy across ice shelf grounding lines and further seawards is important to help constrain ocean-induced melting and associated stability.
Here, we present preliminary results of synthesizing information from radar stratigraphic characteristics from airborne and ground-based radar surveys that have been collected for specific projects starting from the 1990s onwards focusing on ice marginal zones of Antarctica. The key data is based on airborne surveys from the German Alfred Wegener Instituteâs polar aircrafts equipped with a 150 MHz radar. In the meantime this system has been replaced by an ultra-wide band 150-520 MHz radar. The older data will provide a baseline with extensive coverage that can be used for model calibration and change detection over time. We aim to provide metrics of the radio stratigraphy (e.g. shape and slope of internal reflection horizons) as well as classified prevalent stratigraphy types that can be used to calibrate machine learning approaches such as simulation based inference. The data obtained will be integrated in coordination efforts within the SCAR AntArchitecture Action Group
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